In Cixin Liu’s Remembrance of Earth's Past trilogy, why does it take the Trisolaran fleet 400 years to reach the solar system if it can achieve a speed of 1/10 the speed of light, given that Alpha Centauri is only 4.4 light years away? Even accounting for a 1g acceleration then deceleration, wouldn’t it take only 50 years or so?
This apparent paradox is addressed explicitly by Liu when Ye Wenjie is being interrogated. Just as the OP asks:
INTERROGATOR: Then I have a question. If the Trisolaran Fleet that had been launched is capable of flight at one-tenth the speed of light, it should take only forty years to reach the solar system. So why do you say that it would take more than four hundred years?
The answer is:
YE: Here’s the thing. The Trisolaran Interstellar Fleet is composed of incredibly massive spaceships. Accelerating them is a slow process. One-tenth the speed of light is only their maximum speed, but they cannot cruise at this speed for long before decelerating as they approach the Earth. Also, the source of propulsion for the Trisolaran ships is matter-antimatter annihilation. In front of each ship is a large magnetic field shaped like a funnel to collect antimatter particles from space. This collection process is slow, and only after a long wait can it gather enough antimatter to allow the ship to accelerate for a brief period. Thus, the fleet’s acceleration occurs in spurts, interspersed by long periods of coasting to collect fuel. This is why the time it takes the Trisolaran Fleet to reach the solar system is ten times longer than the flight time of a small probe.
This could be a mistake if he assumed a constant acceleration to the mid point and and then constant deceleration to the target (Earth).
The acceleration that would allow a max speed of.15C, where C is the speed of light (3x10^8 m/s) at the center point of the journey, is .005G, where G is 1 Earth gravity (9.8m/s/s). At that acceleration, a trip of 4.4 light years would take 58 years, both Earth time and ship time.
In order for that 4.4 light year journey to take ~450 years, the acceleration would need to be .000086G and the max speed would be .019C.
All this is assuming a constant acceleration. Given this assumption, Cixin Liu's science displays a bit of hand waving and seems to be a plot device. He needed Earth to experience several generations of time to prepare. There are other problems with his story as well, in my opinion, but I'll keep that to myself.
See the relativistic travel calculator below.